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JEE Main 2020 (8 Jan, Shift 2) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from JEE Main 2020 (8 Jan, Shift 2)

Q93JEE Main 2020 · 8 JAN · SHIFT 2Medium

Electric Potential & Equipotentials

Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1 (on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1 (on S1) / V2 (on S2) of the electrostatic potentials on each sphere is:

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Answer: (a)

On a sphere's surface $E = \frac{kQ}{R^2}$ and $V = \frac{kQ}{R}$ , so $V = ER$ .
$\frac{V_1}{V_2} = \frac{E_1}{E_2}\cdot\frac{R_1}{R_2} = \frac{R_1}{R_2}\cdot\frac{R_1}{R_2} = \left(\frac{R_1}{R_2}\right)^2$
So the answer is (a) $(R_1/R_2)^2$ .

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